So i made a k map for each segment and how am i suppose to implement the circuit using only basic gates?
this is what i obtain
a = BA'+ DC'B'+DA'+D'B+CB+D'CA+C'B'A' (' means invert)
b = D'C'+D'B'A'+C'B'+D'BA+C'BA'+DB'A
c = ....
d= ....

I take it your question is about the sheer number of the materials used. Do the restrictions of your exercise prohibit you from using a ready-made bin-to-7seg decoder? If so, consider using groups of gates more than once, ie construct the CB combination needed for a and invert it to use it for the b segment. Or try to find suitable factorizations among the sum elements that can be used by multiple segments.

Think of your circuit as a black box that has 4 inputs and 7 outputs. There's no combining of the segment outputs.

Look at the pdf that Bertus linked to above. They have the internal logic diagram for the 74ls47, which is a bcd-7seg decoder. You just need to change it a bit to display a-f instead of the random symbols it does now.
/mike

Exactly! The datasheet of the 7447 contains a schematic wich is down to the gate level. You could duplicate the exact behaviour of the IC by constructing the gate circuit given. If you want to display A, B, C, etc for numbers larger than 9 however, you need to modify this circuit, wich, I imagine, will require some work, but isn't impossible by any means.